Question

What is the factored form of 2x2 + x – 3?
(2x + 3)(x – 1)
(2x + 1)(x – 3)
(2x – 3)(x + 1)
(2x – 1)(x + 3)

Answer 1

The answer is (2x + 3)(x - 1)

2x² + x - 3 = 2x² +3x - 2x - 3 =
                  = 2x * x - 2x + 3x - 3 =
                  = 2x(x - 1) + 3(x - 1) =
                  = (2x + 3)(x - 1)

Answer 2

Answer:

A. $(x-1)(2x+3)$

Step-by-step explanation:

We are given the quadratic equation $2x^2+x-3$.

We will find the roots of the equation quadratic $2x^2+x-3=0$.

The roots of the quadratic equation $ax^2+bx+c=0$ is given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

On comparing the equations, we get,

a= 2, b= 1, c= -3.

Substituting the values gives us the roots are,

$x=\frac{-1\pm \sqrt{1^2-4\times 2\times (-3)}}{2\times 2}$

i.e. $x=\frac{-1\pm \sqrt{1+24}}{4}$

i.e. $x=\frac{-1\pm \sqrt{25}}{4}$

i.e. $x=\frac{-1\pm 5}{4}$

i.e. $x=\frac{-1+5}{4}$ and $x=\frac{-1-5}{4}$

i.e. $x=\frac{4}{4}$ and $x=\frac{-6}{4}$

i.e. x = 1 and $x=\frac{-3}{2}$

Thus, the factors of the quadratic equation are $(x-1)$ and $(2x+3)[/tex].

Hence, the factored form is [tex](x-1)(2x+3)$.